Quasi-predefined-time control and its comparison with nonlinear active control for hybrid synchronization of identical chaotic systems

Synchronization of chaotic systems provides a promising approach for controlling and regulating complex systems due to its potential in fields ranging from physics to engineering and from biology to finance. Here, a chaotic system for two different initial conditions is synchronized with the help of nonlinear active control and predefined-time control. In the case of nonlinear active control, two control inputs are used, whereas, in predefined-time control, three inputs are considered for convergence of the error dynamics. However, it is found that the control energy requirement is less in the predefined-time control within a comparable convergence time. In addition to the above investigation, a hybrid synchronization, i.e., a combination of phase-synchronization, anti-synchronization, and projective synchronization, is performed by designing a switching control law using a quasi-predefined control technique.